In a network apparatus, it is generally required to collect statistics of some parameters (also referred to as characteristic values). The characteristic values refer to items whose statistics need to be collected. For example, in a network security system, statistics of the number of various connections of a source or destination IP address are collected in order to block Denial of Service (DoS) attacks. As to some characteristic values, thresholds should be set in advance before the statistics are collected. When the statistics of a characteristic value reach or exceed the threshold, some restrictive processing is performed on a process which generates the characteristic value, so as to control the statistics to be within a range and satisfy specific requirements of the network.